Volterra series expansion is a common method describing a nonlinear system, and is featured in that an output value of the system at a certain point in time is related to all input values in a preceding period of time; hence, it is adapted to describe a nonlinear system with a memory effect. And it is frequently used in a communication system to build a model of such a device as a power amplifier, etc.
Currently, a memory nonlinear system may be described by using a Weiner model according to the features thereof. FIG. 1 is a schematic block diagram of a Weiner structure. A module 101 is a linear filter, and let its coefficients be A1, A2 . . . Am, its input signal be Y, and its output signal be X. And a module 102 is a memoryless nonlinear device, and let its coefficients be B0, B1, B2 . . . Bk, its input signal be X, and its output signal be Z.
For module 101, XT=Σi=1mAiYT+1−i, where, XT denotes an output signal of module 101 at a moment T, and YT+1−i denotes an (i−1)-th input signal of module 101 before the moment T, denoting an input signal at the moment T when i=1. For module 102, ZT=B0+Σn=1kBn(XT)n, where, XT denotes an input signal of module 102 at the moment T, and ZT denotes an output signal of module 102 at the moment T. Therefore, the Volterra series expansion of the whole system may be described as:
                              Z          T                =                              B            0                    +                                    ∑                              n                =                1                            k                        ⁢                                                  ⁢                                                            B                  n                                ⁡                                  (                                                            ∑                                              i                        =                        1                                            m                                        ⁢                                                                                  ⁢                                                                  A                        i                                            ⁢                                              Y                                                  T                          +                          1                          -                          i                                                                                                      )                                            n                                                          (        1        )            
FIG. 2 is a schematic diagram of nonlinear modeling of the prior art, giving a general modeling method of a nonlinear model, wherein a module 201 is a nonlinear apparatus/system, a model 202 (nonlinear model terms) is various common nonlinear model expansion terms (such as Volterra series expansion), a module 203 performs calculation, and a module 204 obtains a nonlinear model. Therefore, a nonlinear model may be obtained by using measurement data to calculate (such as methods of RLS, and MLS, etc.) coefficients of various nonlinear terms.
However, it was found by the inventors that the number of the terms of Volterra series is exponentially increased as the increase of the memory length and number of orders of a model, so that the complexity of the model is greatly increased, thereby lowering the application value of the model. The method shown in FIG. 2 does not screen the nonlinear terms of the system according to characteristics of the system, which may bring problems such as over-training, in addition to excessive terms and high complexity, causing the precision of the model to be lowered.
Documents advantageous to the understanding of the present invention and the prior art are listed below, which are incorporated herein by reference, as they are fully described herein.    Document 1: D. Morgan, Z. Ma, J. Kim, M. Zierdt, and J. Pastalan, “A generalized memory polynomial model for digital predistortion of RF power amplifiers,” IEEE Trans. Signal Process., vol. 54, no. 10, pp. 3852-3860, October 2006.); and    Document 2: Adaptive Filter Theory, Simon Haykin, translated by Baoyu Zheng, et al.; ISBN: 9787121106651, May 1, 2010, Publishing House of Electronics Industry.